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MATH 101 HOMEWORK 9 Due on Wednesday Nov. 24, 2004. For full credit, show all work. Calculators are not allowed, except as indicated below. 1. (5 marks) Find the mass of a circular cone of base radius 10 cm and height 20 cm, if its density at a point P is 1 + r/100, where r is the distance from P to the axis of the cone. (You may use a calculator to finish the computations.) 2. (10 marks) Find the centroids of the following planar regions. (a) The region enclosed between the parabola y = 3x − x2 and the line y = 2x − 6. (b) The region in Figure 7.41(d) in the textbook (page 442). 3. (5 marks) A random variable X has probability density f (x) = Cx2 on [0, 1], for some value of C. Find this C. For this C, find the mean value of X. This homework covers Sections 7.4, 7.5 (skip Pappus’s theorem), and some of 7.8. Additional recommended exercises: Section 7.5: 1–18; Section 7.8: 1–13. 1